Lecture: A Spectrally Accurate Numerical Method For Computing The Bogoliubov-De Gennes Excitations Of Dipolar Bose-Einstein Condensates

Lecturer: Prof. Zhang Yong

Time: 16:00-18:00, June 17^th.

Venue: C302B, Minglilou Building

Bio:

Zhang Yong graduated from the School of Mathematics of Tianjin University in 2007, and received his Ph.D. at Tsinghua University in 2012. He has engaged in postdoctoral research at the University of Vienna in Austria, Rennes University in France, and the Krone Institute of New York University in the United States. In July 2015, he received the Schrödinger Fund supported by the Austrian Natural Science Foundation, and was selected into the National High-level Talent Program in 2018. His research interests are mainly in the numerical calculation and analysis of partial differential equations, especially the design and application of fast algorithms. Professor Zhang Yong has published more than 20 papers in leading academic journals such asSIAM Journal on Scientific Computing,SIAM journal on Applied Mathematics,Multiscale Modeling and Simulation,Mathematics of Computation,Journal of Computational Physics,Computer Physics Communication.

Abstract:

In this lecture, we shall focus on an efficient and robust numerical method to study the elementary excitation of dipolar Bose-Einstein condensates (BEC), which is governed by the Bogoliubov-de Gennes equations (BdGEs) with nonlocal dipole-dipole interaction, around the mean field ground state. Analytical properties of the BdGEs are investigated, which could serve as benchmarks for the numerical methods. To evaluate the nonlocal interactions accurately and efficiently, we propose a new Simple Fourier Spectral Convolution method (SFSC). Then, integrating SFSC with the standard Fourier spectral method for spatial discretization and Implicitly Restarted Arnoldi Methods (IRAM) for the eigenvalue problem, we derive an efficient and spectrally accurate method, named as SFSC-IRAM method, for the BdGEs. Ample numerical tests are provided to illustrate the accuracy and efficiency. Finally, we apply the new method to study systematically the excitation spectrum and Bogoliubov amplitudes around the ground state with different parameters in different spatial dimensions.

Organizer and sponsor:

School of Sciences

Institute of Artificial Intelligence

Institute of Nonlinear Dynamical Systems

Mathematical Mechanics Research Center

Institute of Science and Technology Development